Accurate estimation of the internal states of lithiumion batteries is key towards improving their management for safety, efficiency and longevity purposes. Various approaches exist in the literature in this context, among which designing an observer based on an electrochemical model of the battery dynamics. With this approach, the performance of the observer depends on the accuracy of the considered model. It appears that electrochemical models, and thus their associated observers, typically require to be of high dimension to generate accurate internal variables. In this work, we present a method to mitigate this limitation by correcting the lithium concentrations generated by a general class of finite-dimensional electrochemical models such that they asymptotically match those generated by the original partial differential equations (PDE) they are based on, for constant input currents. These corrections apply to finitedimensional models of any order of the considered class. The proposed corrections lead to a new state space model for which we design observers, whose global, robust convergences are supported by a Lyapunov analysis. Both numerical and experimental validations are presented, which show the improvement of the accuracy of the state estimates as a result of the proposed corrections.